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Direct methods for solving the standard or generalized eigenvalue problems <math> Ax = \lambda x</math> and <math> Ax = \lambda B x </math>
are based on transforming the problem to [[Schur form|Schur]] or [[Generalized Schur form]]. However, there is no analogous form for quadratic matrix polynomials.
One approach is to transform the quadratic matrix polynomial to a linear matrix pencil (<math> A-\lambda B</math>), and solve a generalized
eigenvalue problem. Once eigenvalues and eigenvectors of the linear problem have been determined, eigenvectors and eigenvalues of the quadratic can be determined.
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